Season the pork chops generously with salt and black pepper on both sides.
Heat olive oil and butter in a large skillet over medium-high heat (if you have an iron one, that’s best).
Add the pork chops to the skillet and cook for about 4-5 minutes per side, or until browned. Remove the pork chops from the skillet and set them aside.
In the same skillet, add the sliced onion and minced garlic. Cook until the onions are softened and fragrant, about 2-3 minutes.
Stir in the chopped sage leaves and cook for another minute.
Pour in the apple cider, brown sugar, and chicken broth, scraping any browned bits from the bottom of the skillet to incorporate the flavors.
Bring the mixture to a simmer and return the pork chops to the skillet, nestling them in the liquid.
Cover the skillet and let the pork chops simmer in the apple cider mixture for about 10-12 minutes, or until the internal temperature of the pork reaches 145°F.
Remove the pork chops from the skillet and let them rest for a few minutes before serving.
Meanwhile, increase the heat to medium-high and simmer the apple cider sauce uncovered for a few minutes until it has reduced and thickened slightly.
Serve the apple cider sage pork chops with the sauce drizzled over the top and extra on the side.